Question

${\textbf{Subject : Mathematics}}$

${\textbf{Chapter : Tangency}}$


A point P is 13 cm from the centre of the circle. The length of tangent drawn from P to the circle is 12 cm. Find the radius of the circle.​

Answer 1

Hey !

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Given : P is a point at distance of 13cm from the centre of a circle O. The length of tangent drawn from P to the circle is 12 cm.

It is required to measure the radius of the circle.

Now, ∠OTP= 90°

( ∵ a tangent to a circle is ⊥ to the radius through the point of contact).

∴ In right angle triangle OTP,

OP² = OT²+ TP²

Or, 13² = OT² + (12)²

Or, 169-144 = OT²

Or, 25 = OT²

∴ OT = 5 cm

Hence, Radius = 5 cm

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Thanks !

Answer 2

Answer

Circle be O.

Tangent be PQ.

Therfore,

*PO = 13 centimeters

*PQ = 12 centimeters

Radius is perpendicular to tangent at point of meeting of contact

hence, angle OQP = 90 degree

Pythagoras Theorem,

(OP)2 = (OQ)2 + (PQ)2

132 = (OQ)2 + 122

169 - 144 = (OQ)2

(OQ)2 = 25

OQ = 5 cm

$5cm \: is \: the \: radius \: of \: the \: circle$